{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "'''\n",
    "【课程3.2.2】  线性回归的python实现方法\n",
    "\n",
    "线性回归通常是人们在学习预测模型时首选的技术之一。在这种技术中，因变量是连续的，自变量可以是连续的也可以是离散的，回归线的性质是线性的。\n",
    "线性回归使用最佳的拟合直线（也就是回归线）在因变量（Y）和一个或多个自变量（X）之间建立一种关系\n",
    "\n",
    "简单线性回归 / 多元线性回归 \n",
    "\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xbe75208>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98afb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 简单线性回归（一元线性回归）\n",
    "# （1）数据示例\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "# 导入线性回归模块\n",
    "\n",
    "rng = np.random.RandomState(1)  \n",
    "xtrain = 10 * rng.rand(30)\n",
    "ytrain = 8 + 4 * xtrain + rng.rand(30)\n",
    "# np.random.RandomState → 随机数种子，对于一个随机数发生器，只要该种子（seed）相同，产生的随机数序列就是相同的\n",
    "# 生成随机数据x与y\n",
    "# 样本关系：y = 8 + 4*x\n",
    "\n",
    "fig = plt.figure(figsize =(12,3))\n",
    "ax1 = fig.add_subplot(1,2,1)\n",
    "plt.scatter(xtrain,ytrain,marker = '.',color = 'k')\n",
    "plt.grid()\n",
    "plt.title('样本数据散点图')\n",
    "# 生成散点图\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(xtrain[:,np.newaxis],ytrain)\n",
    "# LinearRegression → 线性回归评估器，用于拟合数据得到拟合直线\n",
    "# model.fit(x,y) → 拟合直线，参数分别为x与y\n",
    "# x[:,np.newaxis] → 将数组变成(n,1)形状\n",
    "\n",
    "xtest = np.linspace(0,10,1000)\n",
    "ytest = model.predict(xtest[:,np.newaxis])\n",
    "# 创建测试数据xtest，并根据拟合曲线求出ytest\n",
    "# model.predict → 预测\n",
    "\n",
    "ax2 = fig.add_subplot(1,2,2)\n",
    "plt.scatter(xtrain,ytrain,marker = '.',color = 'k')\n",
    "plt.plot(xtest,ytest,color = 'r')\n",
    "plt.grid()\n",
    "plt.title('线性回归拟合')\n",
    "# 绘制散点图、线性回归拟合直线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xbf05438>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc06f390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 简单线性回归（一元线性回归）\n",
    "# （2）误差\n",
    "\n",
    "rng = np.random.RandomState(8)\n",
    "xtrain = 10 * rng.rand(15)\n",
    "ytrain = 8 + 4 * xtrain + rng.rand(15) * 30\n",
    "model.fit(xtrain[:,np.newaxis],ytrain)\n",
    "xtest = np.linspace(0,10,1000)\n",
    "ytest = model.predict(xtest[:,np.newaxis])\n",
    "# 创建样本数据并进行拟合\n",
    "\n",
    "plt.plot(xtest,ytest,color = 'r',linestyle = '--')  # 拟合直线\n",
    "plt.scatter(xtrain,ytrain,marker = '.',color = 'k')  # 样本数据散点图\n",
    "ytest2 = model.predict(xtrain[:,np.newaxis])  # 样本数据x在拟合直线上的y值\n",
    "plt.scatter(xtrain,ytest2,marker = 'x',color = 'g')   # ytest2散点图\n",
    "plt.plot([xtrain,xtrain],[ytrain,ytest2],color = 'gray')  # 误差线\n",
    "plt.grid()\n",
    "plt.title('误差')\n",
    "# 绘制图表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "斜率a为：4.0045\n",
      "截距b为：8.4477\n",
      "线性回归函数为：\n",
      "y = 4.0045x + 8.4477\n"
     ]
    }
   ],
   "source": [
    "# 简单线性回归（一元线性回归）\n",
    "# （3）求解a，b\n",
    "\n",
    "rng = np.random.RandomState(1)  \n",
    "xtrain = 10 * rng.rand(30)\n",
    "ytrain = 8 + 4 * xtrain + rng.rand(30)\n",
    "# 创建数据\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(xtrain[:,np.newaxis],ytrain)\n",
    "# 回归拟合\n",
    "\n",
    "print('斜率a为：%.4f' % model.coef_[0])\n",
    "print('截距b为：%.4f' % model.intercept_)\n",
    "print('线性回归函数为：\\ny = %.4fx + %.4f' % (model.coef_[0],model.intercept_))\n",
    "# 参数输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         b1        b2        b3        b4          y\n",
      "0  2.219932  8.707323  2.067192  9.186109  60.034105\n",
      "1  4.884112  6.117439  7.659079  5.184180  24.477270\n",
      "2  2.968005  1.877212  0.807413  7.384403  47.129990\n",
      "3  4.413092  1.583099  8.799370  2.740865   2.810948\n",
      "4  4.142350  2.960799  6.287879  5.798378  24.378742\n",
      "斜率a为： [ 1.5  2.  -4.   3. ]\n",
      "截距b为：20.0000\n",
      "线性回归函数为：\n",
      "y = 1.5x1 + 2.0x2 + -4.0x3 + 3.0x4 + 20.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbf92470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 多元线性回归\n",
    "\n",
    "rng = np.random.RandomState(5)  \n",
    "xtrain = 10 * rng.rand(150,4)\n",
    "ytrain = 20 + np.dot(xtrain ,[1.5,2,-4,3])\n",
    "df = pd.DataFrame(xtrain, columns = ['b1','b2','b3','b4'])\n",
    "df['y'] = ytrain\n",
    "pd.scatter_matrix(df[['b1','b2','b3','b4']],figsize=(10,6),\n",
    "                 diagonal='kde',\n",
    "                 alpha = 0.5,\n",
    "                 range_padding=0.1)\n",
    "print(df.head())\n",
    "# 创建数据，其中包括4个自变量\n",
    "# 4个变量相互独立\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(df[['b1','b2','b3','b4']],df['y'])\n",
    "# 多元回归拟合\n",
    "\n",
    "print('斜率a为：' ,model.coef_)\n",
    "print('截距b为：%.4f' % model.intercept_)\n",
    "print('线性回归函数为：\\ny = %.1fx1 + %.1fx2 + %.1fx3 + %.1fx4 + %.1f' \n",
    "      % (model.coef_[0],model.coef_[1],model.coef_[2],model.coef_[3],model.intercept_))\n",
    "# 参数输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "'''\n",
    "【课程3.2.3】  线性回归模型评估\n",
    "\n",
    "通过几个参数验证回归模型\n",
    "\n",
    "SSE(和方差、误差平方和)：The sum of squares due to error\n",
    "MSE(均方差、方差)：Mean squared error\n",
    "RMSE(均方根、标准差)：Root mean squared error\n",
    "R-square(确定系数) Coefficient of determination\n",
    "\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "均方差MSE为: 0.78471\n",
      "均方根RMSE为: 0.88584\n",
      "确定系数R-square为: 0.99465\n"
     ]
    }
   ],
   "source": [
    "# 模型评价\n",
    "# MSE, RMES, R-square\n",
    "\n",
    "from sklearn import metrics\n",
    "\n",
    "rng = np.random.RandomState(1)  \n",
    "xtrain = 10 * rng.rand(30)\n",
    "ytrain = 8 + 4 * xtrain + rng.rand(30) * 3\n",
    "# 创建数据\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(xtrain[:,np.newaxis],ytrain)\n",
    "# 多元回归拟合\n",
    "\n",
    "ytest = model.predict(xtrain[:,np.newaxis])  # 求出预测数据\n",
    "mse = metrics.mean_squared_error(ytrain,ytest)  # 求出均方差\n",
    "rmse = np.sqrt(mse)  # 求出均方根\n",
    "\n",
    "#ssr = ((ytest - ytrain.mean())**2).sum()  # 求出预测数据与原始数据均值之差的平方和\n",
    "#sst = ((ytrain - ytrain.mean())**2).sum()  # 求出原始数据和均值之差的平方和\n",
    "#r2 = ssr / sst # 求出确定系数\n",
    "\n",
    "r2 = model.score(xtrain[:,np.newaxis],ytrain)  # 求出确定系数\n",
    "print(\"均方差MSE为: %.5f\" % mse)\n",
    "print(\"均方根RMSE为: %.5f\" % rmse)\n",
    "print(\"确定系数R-square为: %.5f\" % r2)\n",
    "# 确定系数R-square非常接近于1，线性回归模型拟合较好"
   ]
  }
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